Completability and optimal factorization norms in tensor products of Banach function spaces

[EN] Given s-finite measure spaces ( 1, 1, mu 1) and ( 2, 2, mu 2), we consider Banach spaces X1(mu 1) and X2(mu 2), consisting of L0(mu 1) and L0(mu 2) measurable functions respectively, and study when the completion of the simple tensors in the projective tensor product X1(mu 1). p X2(mu 2) is continuously included in the metric space of measurable functions L0(mu 1. mu 2). In particular, we prove that the elements of the completion of the projective tensor product of L p-spaces are measurable functions with respect to the product measure. Assuming certain conditions, we finally showthat given a bounded linear operator T : X1(mu 1). p X2(mu 2). E (where E is a Banach space), a norm can be found for T to be bounded, which is ` minimal' with respect to a given property (2-rectangularity). The same technique may work for the case of n-spaces.J. M. Calabuig and M. Fernandez-Unzueta were supported by Ministerio de Economia, Industria y Competitividad (Spain) under project MTM2014-53009-P. M. Fernandez-Unzueta was also suported by CONACyT 284110. F. Galaz-Fontes was supported by Ministerio de Ciencia e Innovacion (Spain) and FEDER under project MTM2009-14483-C02-01. E. A. Sanchez Perez was supported by Ministerio de Economia, Industria y Competitividad (Spain) and FEDER under project MTM2016-77054-C2-1-P.Calabuig, JM.; Fernández-Unzueta, M.; Galaz-Fontes, F.; Sánchez Pérez, EA. (2019). Completability and optimal factorization norms in tensor products of Banach function spaces. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 113(4):3513-3530. https://doi.org/10.1007/s13398-019-00711-7S351335301134Abramovich, Y.A., Aliprantis, C.D.: An invitation to operator theory. Graduate Studies in Mathematics, Vol 50, AMS (2002)Bennett, C., Sharpley, R.: Interpolation of Operators. Academic Press, Boston (1988)Bu, Q., Buskes, G., Kusraev, A.G.: Bilinear maps on products of vector lattices: a survey. In: Boulabiar, K., Buskes, G., Triki, A. (eds.) Positivity-Trends in Mathematics. Birkhäser Verlag AG, Basel, pp. 97–26 (2007)Buskes, G., Van Rooij, A.: Bounded variation and tensor products of Banach lattices. Positivity 7, 47–59 (2003)Calabuig, J.M., Fernández-Unzueta, M., Galaz-Fontes, F., Sánchez-Pérez, E.A.: Extending and factorizing bounded bilinear maps defined on order continuous Banach function spaces. RACSAM 108(2), 353–367 (2014)Calabuig, J.M., Fernández-Unzueta, M., Galaz-Fontes, F., Sánchez-Pérez, E.A.: Equivalent norms in a Banach function space and the subsequence property. J. Korean Math. Soc. https://doi.org/10.4134/JKMS.j180682Curbera, G.P., Ricker, W.J.: Optimal domains for kernel operators via interpolation. Math. Nachr. 244, 47–63 (2002)Curbera, G.P., Ricker, W.J.: Vector measures, integration and applications. In: Positivity. Birkhäuser Basel, pp. 127–160 (2007)Gil de Lamadrid, J.: Uniform cross norms and tensor products. J. Duke Math. 32, 797–803 (1965)Dunford, N., Schwartz, J.: Linear Operators, Part I: General Theory. Interscience Publishers Inc., New York (1958)Fremlin, D.H.: Tensor products of Archimedean vector lattices. Am. J. Math. 94(3), 777–798 (1972)Fremlin, D.H.: Tensor products of Banach lattices. Math. Ann. 211(2), 87–106 (1974)Yew, K.L.: Completely $$p$$-summing maps on the operator Hilbert space OH. J. Funct. Anal. 255, 1362–1402 (2008)Kwapien, S., Pelczynski, A.: The main triangle projection in matrix spaces and its applications. Stud. Math. 34(1), 43–68 (1970)Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II. Springer, Berlin (1979)Luxemburg, W.A.J., Zaanen, A.C.: Riesz Spaces I. North-Holland Publishing Company, Amsterdam (1971)Milman, M.: Some new function spaces and their tensor products. Depto. de Matemática, Facultad de Ciencias, U. de los Andes, Mérida, Venezuela (1978)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal domain and integral extension of operators acting in function spaces. Oper. Theory Adv. Appl., vol. 180. Birkhäuser, Basel (2008)Schep, A.R.: Factorization of positive multilinear maps. Illinois J. Math. 579–591 (1984)Zaanen, A.C.: Integration. North-Holland Publishing Company, Amsterdam-New York (1967)Zaanen, A.C.: Riesz Spaces II. North-Holland Publishing Company, Amsterdam (1983

Enabling semantic queries across federated bioinformatics databases

MOTIVATION: Data integration promises to be one of the main catalysts in enabling new insights to be drawn from the wealth of biological data available publicly. However, the heterogeneity of the different data sources, both at the syntactic and the semantic level, still poses significant challenges for achieving interoperability among biological databases. RESULTS: We introduce an ontology-based federated approach for data integration. We applied this approach to three heterogeneous data stores that span different areas of biological knowledge: (i) Bgee, a gene expression relational database; (ii) Orthologous Matrix (OMA), a Hierarchical Data Format 5 orthology DS; and (iii) UniProtKB, a Resource Description Framework (RDF) store containing protein sequence and functional information. To enable federated queries across these sources, we first defined a new semantic model for gene expression called GenEx. We then show how the relational data in Bgee can be expressed as a virtual RDF graph, instantiating GenEx, through dedicated relational-to-RDF mappings. By applying these mappings, Bgee data are now accessible through a public SPARQL endpoint. Similarly, the materialized RDF data of OMA, expressed in terms of the Orthology ontology, is made available in a public SPARQL endpoint. We identified and formally described intersection points (i.e. virtual links) among the three data sources. These allow performing joint queries across the data stores. Finally, we lay the groundwork to enable nontechnical users to benefit from the integrated data, by providing a natural language template-based search interface

Under-five mortality: spatial-temporal clusters in Ifakara HDSS in South-eastern Tanzania.

BACKGROUND\ud \ud Childhood mortality remains an important subject, particularly in sub-Saharan Africa where levels are still unacceptably high. To achieve the set Millennium Development Goals 4, calls for comprehensive application of the proven cost-effective interventions. Understanding spatial clustering of childhood mortality can provide a guide in targeting the interventions in a more strategic approach to the population where mortality is highest and the interventions are most likely to make an impact.\ud \ud METHODS\ud \ud Annual child mortality rates were calculated for each village, using person-years observed as the denominator. Kulldorff's spatial scan statistic was used for the identification and testing of childhood mortality clusters. All under-five deaths that occurred within a 10-year period from 1997 to 2006 were included in the analysis. Villages were used as units of clusters; all 25 health and demographic surveillance sites (HDSS) villages in the Ifakara health and demographic surveillance area were included.\ud \ud RESULTS\ud \ud Of the 10 years of analysis, statistically significant spatial clustering was identified in only 2 years (1998 and 2001). In 1998, the statistically significant cluster (p < 0.01) was composed of nine villages. A total of 106 childhood deaths were observed against an expected 77.3. The other statistically significant cluster (p < 0.05) identified in 2001 was composed of only one village. In this cluster, 36 childhood deaths were observed compared to 20.3 expected. Purely temporal analysis indicated that the year 2003 was a significant cluster (p < 0.05). Total deaths were 393 and expected were 335.8. Spatial-temporal analysis showed that nine villages were identified as statistically significant clusters (p < 0.05) for the period covering January 1997-December 1998. Total observed deaths in this cluster were 205 while 150.7 were expected.\ud \ud CONCLUSION\ud \ud There is evidence of spatial clustering in childhood mortality within the Ifakara HDSS. Further investigations are needed to explore the source of clustering and identify strategies of reaching the cluster population with the existing effective interventions. However, that should happen alongside delivery of interventions to the broader population

Anthracological evidence suggests naturalness of Pinus pinaster in inland southwestern Iberia

The study of well-preserved archaeological charcoals in the pre-Roman Iron Age settlement of Castillejos II (Badajoz, Spain) is used to reconstruct environmental conditions and land-use practices in vegetation landscapes in the southwest of the Iberian Peninsula before the arrival of Roman civilization. The results support that, while evergreen Quercus forests dominated during the Holocene, Pinus pinaster existed as a natural element of southwestern Iberian Peninsula vegetation. Although its presence could be linked to anthropogenic disturbance or fire history, it is suggested that P. pinaster populations survived during the Holocene in the region, mixed with oaks or in monospecific stands in mountain enclaves. This hypothesis contrasts with previous assumptions that P. pinaster was not autochthonous in the area

Co-firing of biomass with coals Part 1. Thermogravimetric kinetic analysis of combustion of fir (abies bornmulleriana) wood

The chemical composition and reactivity of fir (Abies bornmulleriana) wood under non-isothermal thermogravimetric (TG) conditions were studied. Oxidation of the wood sample at temperatures near 600 A degrees C caused the loss of aliphatics from the structure of the wood and created a char heavily containing C-O functionalities and of highly aromatic character. On-line FTIR recordings of the combustion of wood indicated the oxidation of carbonaceous and hydrogen content of the wood and release of some hydrocarbons due to pyrolysis reactions that occurred during combustion of the wood. TG analysis was used to study combustion of fir wood. Non-isothermal TG data were used to evaluate the kinetics of the combustion of this carbonaceous material. The article reports application of Ozawa-Flynn-Wall model to deal with non-isothermal TG data for the evaluation of the activation energy corresponding to the combustion of the fir wood. The average activation energy related to fir wood combustion was 128.9 kJ/mol, and the average reaction order for the combustion of wood was calculated as 0.30

A compact statistical model of the song syntax in Bengalese finch

Songs of many songbird species consist of variable sequences of a finite number of syllables. A common approach for characterizing the syntax of these complex syllable sequences is to use transition probabilities between the syllables. This is equivalent to the Markov model, in which each syllable is associated with one state, and the transition probabilities between the states do not depend on the state transition history. Here we analyze the song syntax in a Bengalese finch. We show that the Markov model fails to capture the statistical properties of the syllable sequences. Instead, a state transition model that accurately describes the statistics of the syllable sequences includes adaptation of the self-transition probabilities when states are repeatedly revisited, and allows associations of more than one state to the same syllable. Such a model does not increase the model complexity significantly. Mathematically, the model is a partially observable Markov model with adaptation (POMMA). The success of the POMMA supports the branching chain network hypothesis of how syntax is controlled within the premotor song nucleus HVC, and suggests that adaptation and many-to-one mapping from neural substrates to syllables are important features of the neural control of complex song syntax

Accuracy of magnetic resonance studies in the detection of chondral and labral lesions in femoroacetabular impingement : systematic review and meta-analysis

Background: Several types of Magnetic resonance imaging (MRI) are commonly used in imaging of femoroacetabular impingement (FAI), however till now there are no clear protocols and recommendations for each type. The aim of this meta-analysis is to detect the accuracy of conventional magnetic resonance imaging (cMRI), direct magnetic resonance arthrography (dMRA) and indirect magnetic resonance arthrography (iMRA) in the diagnosis of chondral and labral lesions in femoroacetabular impingement (FAI). Methods: A literature search was finalized on the 17th of May 2016 to collect all studies identifying the accuracy of cMRI, dMRA and iMRA in diagnosing chondral and labral lesions associated with FAI using surgical results (arthroscopic or open) as a reference test. Pooled sensitivity and specificity with 95% confidence intervals using a random-effects meta-analysis for MRI, dMRA and iMRA were calculated also area under receiver operating characteristic (ROC) curve (AUC) was retrieved whenever possible where AUC is equivocal to diagnostic accuracy. Results: The search yielded 192 publications which were reviewed according inclusion and exclusion criteria then 21 studies fulfilled the eligibility criteria for the qualitative analysis with a total number of 828 cases, lastly 12 studies were included in the quantitative meta-analysis. Meta-analysis showed that as regard labral lesions the pooled sensitivity, specificity and AUC for cMRI were 0.864, 0.833 and 0.88 and for dMRA were 0.91, 0.58 and 0.92. While in chondral lesions the pooled sensitivity, specificity and AUC for cMRI were 0.76, 0.72 and 0.75 and for dMRA were 0.75, 0.79 and 0.83, while for iMRA were sensitivity of 0.722 and specificity of 0.917. Conclusions: The present meta-analysis showed that the diagnostic test accuracy was superior for dMRA when compared with cMRI for detection of labral and chondral lesions. The diagnostic test accuracy was superior for labral lesions when compared with chondral lesions in both cMRI and dMRA. Promising results are obtained concerning iMRA but further studies still needed to fully assess its diagnostic accuracy

‘Trendy’ cities: exploring the adoption of different types of social media by Portuguese municipalities

What are the determinants of social media adoption by local government? This ongoing research provides a tentative answer to this question by analysing the 308 municipalities in Portugal. Extending previous analyses of Facebook and/or Twitter usage levels, we examine why local governments adopt a particular social media platform. More concretely, we explore, with statistical analyses, the determinants of the adoption of different types of social media. We investigate the adoption of three extremely popular social media (i.e. Facebook, Twitter and YouTube) as well as possible alternatives to those, more popular, applications. Since these platforms have distinct natures and can serve diverse purposes, we examine to what extent aspects such as local government’s commitment to transparency and participation, administrative capacity, media landscape, and socio-demographic and economic factors can explain the adoption of certain social media platforms. The results show that, indeed, demographic characteristics and administrative capacity are important factors for the adoption of less popular social media. Surprisingly, we also observe a geographical difference in municipalities’ social media adoption, with the south, in this regard, being ‘trendier’, or more innovative, than the north.This paper is a result of the project “SmartEGOV: Harnessing EGOV for Smart Governance (Foundations, methods, Tools)/NORTE-01-0145-FEDER-000037”, supported by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund (EFDR). António Tavares acknowledges the financial support of the Portuguese Foundation for Science and Technology and the Portuguese Ministry of Education and Science through national funds [Grant No. UID/CPO/0758/2019]

Imaging Electronic Correlations in Twisted Bilayer Graphene near the Magic Angle

Twisted bilayer graphene with a twist angle of around 1.1{\deg} features a pair of isolated flat electronic bands and forms a strongly correlated electronic platform. Here, we use scanning tunneling microscopy to probe local properties of highly tunable twisted bilayer graphene devices and show that the flat bands strongly deform when aligned with the Fermi level. At half filling of the bands, we observe the development of gaps originating from correlated insulating states. Near charge neutrality, we find a previously unidentified correlated regime featuring a substantially enhanced flat band splitting that we describe within a microscopic model predicting a strong tendency towards nematic ordering. Our results provide insights into symmetry breaking correlation effects and highlight the importance of electronic interactions for all filling factors in twisted bilayer graphene.Comment: Main text 9 pages, 4 figures; Supplementary Information 25 page